Molten chlorides are promising heat transfer fluids (HTF) and thermal energy storage (TES) materials for third-generation concentrated solar power (CSP) plants. Despite their low cost and wide operating temperature ranges (400–800 °C), structural materials experience severe corrosion in commercially available chloride salts. The understanding of the corrosion mechanisms is therefore critical for successful plant design to ensure constant power generation over the 30 years of expected lifetime. This work investigates the corrosion behavior of ferritic-martensitic P91 steel and Inconel 600 nickel-based alloy in molten NaCl-KCl-MgCl2 (24.5-20.5-55.0 wt%) under isothermal conditions at 700 °C in Ar. For both alloys, the corrosion attack is associated with the selective dissolution of Cr and the removal of Cr-rich carbides from the alloy matrix leaving subsurface voids. The initial “impurity-driven” corrosion mechanism associated with the cathodic reduction of MgOH+ impurities leads to the formation of insoluble MgO on the substrates’ surface. Compositional and microstructural features of the alloys, especially the distribution of Cr-rich carbides as well as the solubility and mobility of carbon within the metallic matrix, are found to significantly affect their corrosion resistance. The experimental observations indicate, that the formation of galvanic pairs and solid-state diffusion mechanisms play a major role regarding the corrosion attack of the alloys. The systematic corrosion experiments conducted in this study indicate a lower corrosiveness of NaCl-KCl-MgCl2 ternary mixture than that of NaCl-KCl binary mixture in static conditions at 700 °C under Ar. This work gives significant insights into corrosion issues that may be expected in third-generation industrial CSP plants.